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08 May 2012, 00:21
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Is \(|x - y| \gt |x + y|\) ?
1) \(x^2 - y^2 = 9\)
2) \(x - y = 2\)
From S1, can we assume that x has to equal 5 and y has to equal 4 so when you square x and y, their difference would be 9. Thus S1 would be sufficient.
S2 is insufficient.
Thus the answer is A, but the Official Answer is C. Can someone please explain. Thanks.
1) \(x^2 - y^2 = 9\)
2) \(x - y = 2\)
From S1, can we assume that x has to equal 5 and y has to equal 4 so when you square x and y, their difference would be 9. Thus S1 would be sufficient.
S2 is insufficient.
Thus the answer is A, but the Official Answer is C. Can someone please explain. Thanks.
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08 May 2012, 00:30
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Samwong
Is \(|x - y| \gt |x + y|\) ?
1) \(x^2 - y^2 = 9\)
2) \(x - y = 2\)
From S1, can we assume that x has to equal 5 and y has to equal 4 so when you square x and y, their difference would be 9. Thus S1 would be sufficient.
S2 is insufficient.
Thus the answer is A, but the Official Answer is C. Can someone please explain. Thanks.
1) \(x^2 - y^2 = 9\)
2) \(x - y = 2\)
From S1, can we assume that x has to equal 5 and y has to equal 4 so when you square x and y, their difference would be 9. Thus S1 would be sufficient.
S2 is insufficient.
Thus the answer is A, but the Official Answer is C. Can someone please explain. Thanks.
Why would you assume that? Why not x=-5 and y=-4? Or x=3 and y=0? \(x^2 - y^2 = 9\) has infinitely many solutions for x and y, and only one of them is x=5 and y=4.
Is \(|x - y| \gt |x + y|\) ?
(1) \(x^2 - y^2 = 9\) --> \((x-y)(x+y)=9\). Not sufficient.
(2) \(x - y = 2\) --> don't know the value of \(x+y\). Not sufficient.
(1)+(2) Since from (2) \(x - y = 2\) then from (1) \((x-y)(x+y)=2(x+y)=9\) --> \(x+y=4.5\). Sufficient.
Answer: C.
Hope it helps.
08 May 2012, 00:54
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Thanks Bunuel for the reply. That make sense now. I did a similar problem on MGMAT CAT. The difference is that on the MGMAT problem there is a constrain of x < y < 0
If x and y are integers such that x < y < 0, what is x – y?
(1) (x + y)(x – y) = 5
(2) xy = 6
Official Explanation:
The problem stem tells you that x and y are both negative integers, and x is less than y. You are asked for the value of x – y. Note that in order to answer this question, you might not need the separate values of x and y; however, if you can find those separate values, then you can solve for x – y or any other “combo.”
(1) SUFFICIENT: This statement is tricky. One approach is to distribute the left side to get the difference of squares:
x2 – y2 = 5
Now, since both x and y are integers, x2 and y2 are integers as well. Let’s look at the sequence of squares, and consider their differences (we can leave out zero, since neither x nor y can be zero):
1 4 9 16 25 36…
Diff = 3 5 7 9 11…
As you can see, the difference between squares grows as the squares themselves get larger. The only difference between two squares that equals 5 is the difference between 4 and 9. Since x and y are both negative, this tells us that x = –3 and y = –2; therefore, x – y = –1.
Alternatively, we could note that both x + y and x – y are themselves integers. Looking at the statement, we have
(x + y)(x – y) = 5
int × int = 5
The only possible integer pairs that give 5 as a product are (5, 1) and (-5, -1), since 5 is prime. Now, because both x and y are negative, the (5, 1) pair won’t work either way (either with x + y = 5 or with x + y = 1). So let’s try (-5, -1):
x + y = –5
x – y = –1
Adding these two equations, we get 2x = -6, or x = -3. Substituting back into x + y = –5, we get y = –2. (If we had assigned x + y = –1 and x – y = –5, we would have gotten y = 2, which doesn’t fit the problem constraints.)
(2) INSUFFICIENT: There are two pairs of integers that fit the constraint x < y < 0 and the statement xy = 6: (-3)(-2) = 6 AND (-6)(-1) = 6.
The correct answer is A.
If x and y are integers such that x < y < 0, what is x – y?
(1) (x + y)(x – y) = 5
(2) xy = 6
Official Explanation:
The problem stem tells you that x and y are both negative integers, and x is less than y. You are asked for the value of x – y. Note that in order to answer this question, you might not need the separate values of x and y; however, if you can find those separate values, then you can solve for x – y or any other “combo.”
(1) SUFFICIENT: This statement is tricky. One approach is to distribute the left side to get the difference of squares:
x2 – y2 = 5
Now, since both x and y are integers, x2 and y2 are integers as well. Let’s look at the sequence of squares, and consider their differences (we can leave out zero, since neither x nor y can be zero):
1 4 9 16 25 36…
Diff = 3 5 7 9 11…
As you can see, the difference between squares grows as the squares themselves get larger. The only difference between two squares that equals 5 is the difference between 4 and 9. Since x and y are both negative, this tells us that x = –3 and y = –2; therefore, x – y = –1.
Alternatively, we could note that both x + y and x – y are themselves integers. Looking at the statement, we have
(x + y)(x – y) = 5
int × int = 5
The only possible integer pairs that give 5 as a product are (5, 1) and (-5, -1), since 5 is prime. Now, because both x and y are negative, the (5, 1) pair won’t work either way (either with x + y = 5 or with x + y = 1). So let’s try (-5, -1):
x + y = –5
x – y = –1
Adding these two equations, we get 2x = -6, or x = -3. Substituting back into x + y = –5, we get y = –2. (If we had assigned x + y = –1 and x – y = –5, we would have gotten y = 2, which doesn’t fit the problem constraints.)
(2) INSUFFICIENT: There are two pairs of integers that fit the constraint x < y < 0 and the statement xy = 6: (-3)(-2) = 6 AND (-6)(-1) = 6.
The correct answer is A.
